CN105699953B - Frequency diversity MIMO radar is apart from the decoupling Beamforming Method of angle - Google Patents
Frequency diversity MIMO radar is apart from the decoupling Beamforming Method of angle Download PDFInfo
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- CN105699953B CN105699953B CN201610058784.2A CN201610058784A CN105699953B CN 105699953 B CN105699953 B CN 105699953B CN 201610058784 A CN201610058784 A CN 201610058784A CN 105699953 B CN105699953 B CN 105699953B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/42—Diversity systems specially adapted for radar
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/28—Details of pulse systems
- G01S7/2813—Means providing a modification of the radiation pattern for cancelling noise, clutter or interfering signals, e.g. side lobe suppression, side lobe blanking, null-steering arrays
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- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
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- Variable-Direction Aerials And Aerial Arrays (AREA)
- Geophysics And Detection Of Objects (AREA)
Abstract
The invention discloses a kind of frequency diversity MIMO radar apart from the decoupling Beamforming Method of angle, mainly solve the problems, such as that existing frequency diversity array cannot be formed apart from the decoupling automated response of angle.Implementation step is：1. design frequency diversity array emitter signal frequency；2. obtain frequency diversity array emitter signal and receiving terminal echo-signal；3. pair receiving terminal echo-signal carries out vector output, the snap vector of echo-signal is obtained；4. pair snap vector carries out Adaptive beamformer, obtain forming directional diagram apart from the two dimensional beam of angle.The present invention makes full use of the frequency diversity array emitter free degree, form the controllable degrees of freedom tieed up based on frequency diversity MIMO radar system in distance and angle, and formed by the two dimensional beam that Adaptive beamformer technology is realized apart from angle, available for target apart from angle joint-detection, and suppress with apart from relevant interference signal.
Description
Technical field
The invention belongs to signal processing technology field, more particularly to a kind of frequency diversity MIMO radar distance-angle decoupling
Beamforming Method is closed, available for detection target and suppression and apart from relevant interference.
Background technology
Multiple-input and multiple-output MIMO radar can effectively utilize the transmitting free degree, in fact compared to traditional phased-array radar
Existing send-receive Combined Treatment, it is possible to increase adaptive ability, improves radar parameter estimation performance.But traditional multi input
Multi output MIMO radar only has the angle dimension free degree, without the distance dimension free degree, it is difficult to realizes with pressing down apart from relevant interference
System.
The concept of frequency diversity array is proposed by Paul Antonik et al. in international radar meeting in 2006, with spirit
Beam steering ability living, increasingly causes the concern of domestic and foreign scholars.Compared to traditional phased-array radar, it respectively launches array element
Carrier frequency there are a small frequency interval, it is possible thereby to produce and distance-angle dependency antenna radiation pattern.Nearly ten years,
Distance-angle two dimensional beam on frequency diversity array radar is formed, ground with characteristics such as the suppression apart from relevant interference
Study carefully.But the distance of frequency diversity array pattern-angle two dimension dependence is determined by frequency increment, it is impossible to is adaptively formed
Zero point and depression, it is poor to the rejection ability of complex environment and interference, the serious of target detection performance can be caused in these cases
Decline, it is therefore desirable to adaptively form the beam pattern to match with environment, enhancing frequency diversity array pattern is multiple
Adaptability under heterocycle border.
The content of the invention
Present invention aims at a kind of decoupling Beamforming Method of frequency diversity MIMO radar distance-angle is proposed, certainly
Adaptation to the ground exists into the uncoupled beam pattern of distance-angle to match with environment, enhancing frequency diversity array pattern
Adaptability under complex environment, improves target detection performance.
Be on the basis of the frequency diversity multiple-input and multiple-output MIMO radar system, to its distance-angle the two-dimensional field from
Adapt to beam-forming technology studied, excavate its distance-angle joint domain carry out target detection and suppression with apart from phase
Close the ability of interference.
The present invention basic ideas be：Under white Gaussian noise background, pass through each transmitting array element to being uniformly distributed linear array
Between pull-in frequency interval, by frequency diversity array emitter orthogonal waveforms signal, pass through and produce and all relevant hair of distance, angle
Steering vector is penetrated, by the Adaptive beamformer skill for using the undistorted response MVDR of minimum variance to echo-signal in receiving terminal
Art, it is possible thereby to produce the antenna radiation pattern with angle, distance while dependence, and then carries out target in distance-angle joint domain
Detection and AF panel.Its implementation is as follows：
(1) the pull-in frequency interval delta f between each transmitting array element of co-located uniform line-array, obtains frequency diversity array m-th
Launch the emission signal frequency of array element：
fm=f0+ (m-1) Δ f, m=1,2 ..., M
Wherein, M is to launch array element number, f0For first antenna, the i.e. carrier frequency of reference antenna；
(2) according to transmitting signal gross energy E and the emission signal frequency f of frequency diversity arraym, obtain m-th of transmitting battle array
The transmitting signal of member：
Wherein, E is to launch signal gross energy, φm(t) it is m-th of array element transmitted waveform, j represents imaginary number, when t is propagates
Between；
(3) frequency diversity array received end echo-signal is obtained：
(3a) obtains the reception signal of n-th of array element of receiving terminal：
Wherein, ym,n(t) signal launched by m-th of array element, n=1,2 ..., N are received by n-th of array element, N is reception
Array-element antenna number；
(3b) structure transmitting steering vector aL(θ, R) and receive steering vector aR(θ)：
Wherein θ represents angle, and R represents distance, dL、dRRespectively launch, receive array element spacing, symbol ⊙ is Hadamard
Hadamard is accumulated, symbol []TRepresent transposition computing；
The each array element received signal of receiving terminal is expressed as matrix form by (3c)：
Wherein, Φ is the matrix of each array element transmitted waveform, and ξ is reflectance factor；
(3d) obtains the synthetic echo signal expression formula of receiving terminal according to (3c)：
Wherein S be receive echo signal matrix, θ0And R0Respectively angle and distance where target, J are the interference received
Signal matrix, θiAnd RiAngle and distance where respectively i-th interference source, D are interference source number, and N is white Gaussian noise, ξs
And ξiRespectively echo signal and the reflectance factor of interference；
Synthetic echo signal X after the Waveform Matching of M roads, then is carried out vector output by (3e), obtains receiving the fast of signal
Clap vector y；
(4) Wave beam forming is carried out according to the reception signal phasor y in (3e)：
(4a) calculates interference plus noise covariance matrix according to the reception signal phasor y in (3e)：
Wherein It is the power of i-th of interference,For noise covariance square
Battle array, symbolIt is Kronecker Kronecker products；
(4b) obtains the solution of the undistorted response of minimum variance according to interference plus noise covariance matrix Q：
Wherein
(4c) obtains the reception beam pattern related with distance, angle according to the solution w of the undistorted response of minimum variance：
F (θ, R)=wTa(θ,R)
Wherein
The present invention has the following advantages compared with prior art：
First, the present invention is by pull-in frequency interval delta f between respectively launching array element in co-located uniform line-array, it is possible thereby to produce
With distance and angle dependency antenna radiation pattern, therefore not only have angle dimension the free degree, but also with distance dimension the free degree.
Second, the present invention can carry out united beam shape by using MIMO technology to frequency diversity array in receiving terminal
Into generation and distance, the uncoupled automated response of angle, can adaptively form the beam direction to match with environment
Figure, adaptability of the enhancing frequency diversity array pattern under complex environment, improves target detection performance.
3rd, the Adaptive beamformer technology of the invention by using the undistorted response of minimum variance, it is possible to achieve away from
Formed from, angle two dimensional beam, realize distance-angle joint-detection of target, it is particularly possible to suppress the interference apart from dependent form.
Brief description of the drawings
Fig. 1 is the usage scenario figure of the present invention；
The Wave beam forming that Fig. 2 is the present invention realizes flow chart；
Fig. 3 is the Wave beam forming power spectrum emulated with the present invention；
Fig. 4 is the Wave beam forming directional diagram emulated with the present invention.
Embodiment
The embodiment of the present invention and effect are described in further detail below in conjunction with the accompanying drawings.
With reference to Fig. 1, usage scenario of the invention is based on frequency diversity MIMO radar system：Assuming that target is located at far field,
The elevation angle is θ, and transmitting terminal is made of M transmitting array element in frequency diversity MIMO radar system, and array element spacing is dL；Receiving terminal is by N
A array element composition, array element spacing is dR；The signal frequency of m-th of array element is：
fm=f0+ (m-1) Δ f, m=1,2 ..., M
Wherein, f0For reference work frequency, Δ f frequency intervals between array element.
With reference to Fig. 2, step is as follows for of the invention realizing：
Step 1, the pull-in frequency interval delta f between each transmitting array element of co-located uniform line-array, obtains frequency diversity array m
The emission signal frequency of a transmitting array element：
fm=f0+ (m-1) Δ f, m=1,2 ..., M
Wherein, M is to launch array element number, f0For first antenna, the i.e. carrier frequency of reference antenna.
Step 2, frequency diversity array emitter signal is obtained.
(2a) obtains the waveform φ of m-th of array element transmitting respectivelym(t) the waveform φ launched with k-th of array elementkAnd φ (t),m
(t) and φk(t) mutually orthogonal, the expression formula of its orthogonality relation is as follows：
Wherein TpFor pulse width, k=1,2 ..., M, symbol []*For conjugate operation.
(2b) is according to the emission signal frequency f of frequency diversity arraymWith m-th of array element transmitted waveform φm(t), m is obtained
The transmitting signal of a transmitting array element：
Wherein, E is transmitting signal gross energy, and j represents imaginary number, and t is the propagation time.
Step 3, frequency diversity array received end echo-signal is obtained.
(3a) calculates the transmitting-receiving round trip time delay for being transmitted to n-th of array element from m-th of array element and receiving：
Wherein θ represents angle, and R represents distance, dL、dRRespectively launch, receive array element spacing, n=1,2 ..., N, N is to connect
Receive array-element antenna number；
(3b) is according to the round trip delay, τ in (3a)m,n, obtain n-th of array element and receive the signal launched by m-th of array element：
(3c) receives the signal y launched by m-th of array element according to n-th of array elementm,n(t), n-th gust of receiving terminal is obtained
The reception signal of member：
(3d) structure transmitting steering vector aL(θ, R) and receive steering vector aR(θ)：
Wherein θ represents angle, and R represents distance, and symbol ⊙ accumulates for Hadamard Hadamard, symbol []TRepresent transposition fortune
Calculate；
According to above-mentioned transmitting, receive steering vector expression formula, transmitting steering vector aL(θ, R) depends on distance and angle,
Receive steering vector aR(θ) only relies upon angle, therefore can effectively utilize the transmitting terminal distance dimension free degree and launch-connect
Combined Treatment is received, realizes that distance-angle is decoupling.
The each array element received signal of receiving terminal is expressed as matrix form by (3e)：
Wherein, Φ is the matrix of each array element transmitted waveform, and ξ is reflectance factor；
(3f) obtains the synthetic echo signal expression formula of receiving terminal according to (3e)：
Wherein S be receive echo signal matrix, θ0And R0Respectively angle and distance where target, J are the interference received
Signal matrix, θiAnd RiAngle and distance where respectively i-th interference source, D are interference source number, and N is white Gaussian noise, ξs
And ξiRespectively echo signal and the reflectance factor of interference, it is related with the scattering properties of target and interference respectively.
Step 4, by the synthetic echo signal X in step (3f) after the Waveform Matching of M roads, then vector output is carried out, obtained
To the snap vector y for receiving signal：
Wherein B is sampling number of snapshots, and g is zero mean Gaussian white noise, symbolIt is Kronecker Kronecker products.
Step 5, Wave beam forming is carried out according to the reception signal phasor y in step 4.
(5a) calculates interference plus noise covariance matrix according to the reception signal phasor y in step 4：
Wherein It is the power of i-th of interference,I is noise covariance square
Battle array；
(5b) obtains the expression formula of the undistorted response of minimum variance according to interference plus noise covariance matrix Q：
WhereinFor steering vector, w is the solution of the undistorted response of minimum variance；
The undistorted response equation group of minimum variance in (5c) solution (5b), so as to obtain the undistorted response of minimum variance
Solution：
Wherein
(5d) obtains the reception beam pattern related with distance, angle according to the solution w of the undistorted response of minimum variance：
F (θ, R)=wTa(θ,R)。
The effect of the present invention is described further below by emulation experiment.
1. simulation parameter：
If the array element of transmitting terminal is 8, array element spacing is dL=0.015m, frequency interval Δ f=3KHz；
If the array element of receiving terminal is 6, array element spacing is dR=0.015m；
Angle and distance where target is respectively θ0=0 ° and R0=30Km, Signal to Noise Ratio (SNR)=20dB；
If there are two interference sources, and the first interference source 1 relies only on and angle, it is θ that it, which disturbs angle,1=20 °, second is dry
Disturb source 2 and depend on angle and distance, it is respectively θ that it, which disturbs angle and distance,0=45 ° and R0=40Km, dry make an uproar compare JNR=30dB.
Above-mentioned simulation parameter is as shown in table 1：
1 system emulation parameter of form
2. emulation content：
Emulation 1, under above-mentioned simulation parameter, using the method for the present invention, emulates power spectrum, the results are shown in Figure 3.
As seen from Figure 3, echo signal and the power spectrum of the second interference 2 show distance-angle coupled characteristic, and the
The power spectrum analogous diagram of one disturbed one only depends on angle.
Emulation 2, under above-mentioned simulation parameter, using the method for the present invention, emulates, as a result such as to receiving beam pattern
Shown in Fig. 4.
As seen from Figure 4, the decoupling Wave beam forming directional diagram of frequency diversity MIMO radar distance-angle of the present invention is not only
It is the function of angle, and and distance dependent, and directional diagram forms main lobe at desired distance and angle, and the shape at interference
Into null, show that the present invention has the ability suppressed with apart from relevant interference.
The correctness of the above-mentioned simulating, verifying present invention, validity and reliability.
Claims (5)
1. the decoupling Beamforming Method of frequency diversity MIMO radar distance-angle, including：
(1) the pull-in frequency interval delta f between each transmitting array element of co-located uniform line-array, obtains frequency diversity array and launches for m-th
The emission signal frequency of array element：
fm=f0+ (m-1) Δ f, m=1,2 ..., M
Wherein, M is to launch array element number, f0For first antenna, the i.e. carrier frequency of reference antenna；
(2) according to transmitting signal gross energy E and the emission signal frequency f of frequency diversity arraym, obtain the hair of m-th of transmitting array element
Penetrate signal：
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Wherein, E is to launch signal gross energy, φm(t) it is m-th of array element transmitted waveform, j expression imaginary numbers, t is the propagation time；
(3) frequency diversity array received end echo-signal is obtained：
(3a) obtains the reception signal of n-th of array element of receiving terminal：
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(3b) structure transmitting steering vector aL(θ, R) and receive steering vector aR(θ)：
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Wherein θ represents angle, and R represents distance, dL、dRRespectively launch, receive array element spacing, symbol ⊙ is Hadamard
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The each array element received signal of receiving terminal is expressed as matrix form by (3c)：
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(3d) obtains the synthetic echo signal expression formula of receiving terminal according to (3c)：
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Matrix, θiAnd RiAngle and distance where respectively i-th interference source, D are interference source number, and N is white Gaussian noise, ξsAnd ξi
Respectively echo signal and the reflectance factor of interference；
Synthetic echo signal X after the Waveform Matching of M roads, then is carried out vector output by (3e), obtains receiving the snap arrow of signal
Measure y；
(4) Wave beam forming is carried out according to the reception signal phasor y in (3e)：
(4a) calculates interference plus noise covariance matrix according to the reception signal phasor y in (3e)：
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(4b) obtains the solution of the undistorted response of minimum variance according to interference plus noise covariance matrix Q：
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<mrow>
<msup>
<mi>a</mi>
<mi>H</mi>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<msub>
<mi>R</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<msup>
<mi>Q</mi>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mi>a</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<msub>
<mi>R</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</mrow>
Wherein
<mrow>
<mi>a</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<msub>
<mi>R</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>a</mi>
<mi>R</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>&CircleTimes;</mo>
<msub>
<mi>a</mi>
<mi>L</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<msub>
<mi>R</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
(4c) obtains the reception beam pattern related with distance, angle according to the solution w of the undistorted response of minimum variance：
F (θ, R)=wTa(θ,R)
Wherein
<mrow>
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>,</mo>
<mi>R</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>a</mi>
<mi>R</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>&CircleTimes;</mo>
<msub>
<mi>a</mi>
<mi>L</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>,</mo>
<mi>R</mi>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
2. the decoupling Beamforming Method of frequency diversity MIMO radar distance-angle according to claim 1, wherein step
(2) m-th of array element transmitted waveform in is φm(t), the waveform of its transmitting with other array elements is mutually orthogonal, i.e., with k-th of array element
The waveform φ of transmittingk(t) orthogonal, the expression formula of the orthogonality relation is as follows：
<mrow>
<msub>
<mo>&Integral;</mo>
<msub>
<mi>T</mi>
<mi>p</mi>
</msub>
</msub>
<msub>
<mi>&phi;</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<msubsup>
<mi>&phi;</mi>
<mi>k</mi>
<mo>*</mo>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>t</mi>
<mo>=</mo>
<mi>&delta;</mi>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>-</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>k</mi>
<mo>=</mo>
<mi>m</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mi>k</mi>
<mo>&NotEqual;</mo>
<mi>m</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein TpFor pulse width, k=1,2 ..., M, symbol []*For conjugate operation.
3. the decoupling Beamforming Method of frequency diversity MIMO radar distance-angle according to claim 1, wherein step
N-th of array element in (3a) receives the signal y launched by m-th of array elementM, n(t), its expression formula is：
<mrow>
<msub>
<mi>y</mi>
<mrow>
<mi>m</mi>
<mo>,</mo>
<mi>n</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msqrt>
<mfrac>
<mi>E</mi>
<mi>M</mi>
</mfrac>
</msqrt>
<msub>
<mi>&phi;</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>m</mi>
<mo>,</mo>
<mi>n</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>exp</mi>
<mo>{</mo>
<mi>j</mi>
<mn>2</mn>
<msub>
<mi>&pi;f</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>m</mi>
<mo>,</mo>
<mi>n</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>}</mo>
</mrow>
Wherein τm,nFor radar signal, round trip time delay is received, its expression formula is：
<mrow>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>m</mi>
<mo>,</mo>
<mi>n</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&lsqb;</mo>
<mi>R</mi>
<mo>-</mo>
<msub>
<mi>d</mi>
<mi>L</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mi>&theta;</mi>
<mo>&rsqb;</mo>
<mo>+</mo>
<mo>&lsqb;</mo>
<mi>R</mi>
<mo>-</mo>
<msub>
<mi>d</mi>
<mi>R</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mi>&theta;</mi>
<mo>&rsqb;</mo>
</mrow>
<mi>c</mi>
</mfrac>
</mrow>
Wherein θ represents angle, and R represents distance, dLAnd dRRespectively launch, receive array element spacing, c is the light velocity.
4. the decoupling Beamforming Method of frequency diversity MIMO radar distance-angle according to claim 1, wherein step
Reception signal snap vector y in (3e), its expression formula are：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>y</mi>
<mo>=</mo>
<mi>v</mi>
<mi>e</mi>
<mi>c</mi>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mi>B</mi>
</mfrac>
<msup>
<mi>X&Phi;</mi>
<mi>H</mi>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<msub>
<mi>&xi;</mi>
<mi>s</mi>
</msub>
<msub>
<mi>a</mi>
<mi>R</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>&CircleTimes;</mo>
<msub>
<mi>a</mi>
<mi>L</mi>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>&theta;</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<msub>
<mi>R</mi>
<mn>0</mn>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>D</mi>
</munderover>
<mrow>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>a</mi>
<mi>R</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mo>&CircleTimes;</mo>
<msub>
<mi>a</mi>
<mi>L</mi>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>g</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein B is sampling number of snapshots, and g is zero mean Gaussian white noise, symbolIt is Kronecker Kronecker products.
5. the decoupling Beamforming Method of frequency diversity MIMO radar distance-angle according to claim 1, wherein step
According to interference plus noise covariance matrix Q in (4b), the solution w of the obtained undistorted response of minimum variance, is by solving as follows most
The small undistorted response equation group of variance obtains：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<munder>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
<mi>w</mi>
</munder>
<mo>{</mo>
<msup>
<mi>w</mi>
<mi>H</mi>
</msup>
<mi>Q</mi>
<mi>w</mi>
<mo>}</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>w</mi>
<mi>H</mi>
</msup>
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>,</mo>
<mi>R</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein
<mrow>
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>,</mo>
<mi>R</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>a</mi>
<mi>R</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>&CircleTimes;</mo>
<msub>
<mi>a</mi>
<mi>L</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>,</mo>
<mi>R</mi>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
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| CN106324568A (en) * | 2016-08-09 | 2017-01-11 | 电子科技大学 | Method for forming transmitting beam of distributed array radar with nonlinear frequency increment |
| CN106529440B (en) * | 2016-11-02 | 2019-08-13 | 西安电子科技大学 | Coincidence frequency diversity battle array radar segmented matched filter method |
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| CN107657070B (en) * | 2017-07-31 | 2021-05-25 | 西安电子科技大学 | Decoupling method and antenna based on frequency diversity conformal array beam of genetic algorithm |
| CN108594186B (en) * | 2017-08-25 | 2020-04-07 | 西安电子科技大学 | Method for inhibiting main lobe deceptive interference by FDA-MIMO radar |
| CN107656257B (en) * | 2017-09-28 | 2021-03-23 | 西安电子科技大学 | Optimization design method for missile-borne MIMO radar waveform covariance matrix |
| CN108196239B (en) * | 2018-01-18 | 2022-03-18 | 西安电子科技大学 | Unambiguous parameter estimation method for frequency diversity MIMO radar |
| CN108776337B (en) * | 2018-04-24 | 2021-11-05 | 桂林电子科技大学 | MIMO-FDA ground penetrating radar near-target two-dimensional imaging method |
| CN108919205B (en) * | 2018-07-12 | 2022-07-08 | 中国船舶重工集团公司第七二四研究所 | Frequency diversity array deception jamming suppression method based on auxiliary array elements |
| CN109633572B (en) * | 2018-12-20 | 2022-09-06 | 桂林电子科技大学 | Complex environment fixed-point interference signal design method based on frequency diversity array |
| CN109901149B (en) * | 2019-03-25 | 2022-10-28 | 西安电子科技大学 | Target parameter estimation method based on FDA-MIMO radar |
| CN109917340B (en) * | 2019-04-25 | 2023-05-09 | 浙江力邦合信智能制动系统股份有限公司 | MIMO radar waveform modulation and demodulation method |
| CN110346764B (en) * | 2019-08-21 | 2022-03-29 | 上海无线电设备研究所 | MIMO radar target distance angle decoupling method |
| CN110687937B (en) * | 2019-10-14 | 2021-09-28 | 东北大学 | Water tank liquid level control method based on multivariable generalized minimum variance decoupling control |
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